Each face of a conventional six-sided die displays one of six numbers ranging in values from 1 through 6, traditionally represented by funneled dots. Since there are six ways each of three six-sided dice can turn up in a dice roll; 6 (die one).times.6 (die two).times.6 (die three); two-hundred-sixteen possible combinations of three dice will display each of the normally expected sixteen numerical sums, ranging in values from three through eighteen.
The renowned Italian Scientist, Galilei Galileo (1564-1642), notably recognized as an astronomer, philosopher, physicist and mathematician, is credited for having established the odds or probabilities that occur when three dice are simultaneously rolled out over an extended period of time, as illustrated in Table I.
TABLE I __________________________________________________________________________ Number Of Ways Each Possible Sum May Be Obtained With 3 Dice Number On Sum Of 3 Dice 3rd Dice 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 __________________________________________________________________________ 1 1 2 3 4 5 6 5 4 3 2 1 2 1 2 3 4 5 6 5 4 3 2 1 3 1 2 3 4 5 6 5 4 3 2 1 4 1 2 3 4 5 6 5 4 3 2 1 5 1 2 3 4 5 6 5 4 3 2 1 6 1 2 3 4 5 6 5 4 3 2 1 Total Number 1+ 3+ 6+ 10+ 15+ 21+ 25+ 27+ 27+ 25+ 21+ 15+ 10+ 6+ 3+ 1 = 216 of Ways combinations __________________________________________________________________________
Examination of the rolled combinations, shows that the normally expected sixteen sums of 3 dice, ranging in values from three through eighteen, turn up for a total of exactly two-hundred-sixteen ways, with each of the sixteen sums rolled out with varying odds as follows: Sums three and eighteen, with odds of 1 in 216; sums four and seventeen, with odds of 1 in 72; sums five and sixteen, with odds of 1 in 36; sums six and fifteen, with odds of 5 in 108; sums seven and fourteen, with odds of 5 in 72; sums eight and thirteen, with odds of 7 in 72; sums nine and twelve, with odds of 25 in 216; and sums ten and eleven, with odds of 1 in 8.
Although Galileo established the odds or probabilities when three six-sided dice are rolled out over an extended period of time, only sixteen numerical sums, out of two-hundred-sixteen rolled combinations, can be visually differentiated with a set of three conventional dice of one color. For example, even though the sums of either ten or eleven can be rolled out in twenty-seven different ways, as illustrated in Table I, with a conventional set of three dice of one color, only one sum of either ten or eleven can be visually differentiated in any kind of game of chance. In other words, even though there are twenty-seven separate ways the sums of either ten or eleven can turn up in a dice roll, there are no games currently available that can be played with a set of three six-sided dice of one color, to visually differentiate the twenty-seven possible ways to obtain the sums of either ten or eleven, or for that matter, any of the combinations for the numerical sums of four, five, six, seven, eight, nine, twelve, thirteen, fourteen, sixteen or seventeen, as shown in Table I.
Since the three dice in a set of conventional dice are of identical color, it is virtually impossible for game participants to visually differentiate each of the two-hundred-sixteen possible rolled combinations that display the sixteen numerical sums, ranging in values from three through eighteen. Without the ability to visually differentiate each of the two-hundred-sixteen possible numerical combinations of three dice, all current dice related games using a conventional set of 3 dice of one color, incorporating various game boards, playing cards or a combination thereof, are limited to only the normally expected sixteen visually discernable numerical scores, each of which turns up with varying odds. As a result, a great number of games currently available, utilize either several six-sided dice or dice with more than six sides, to compensate for the scoring limitation that is clearly evident when either a set of two or three conventional six-sided dies are used in various games of chance.
Color or symbol coding each of the six or more numbered or unnumbered faces on a die or multiples of such dice, as a means to develop specific dice related games, incorporating game boards, playing cards or a combination thereof, is widely exemplified in the patent literature, with specific references cited in U.S. Pat. Nos. 1,481,628; 1,631,505; 2,526,300; 2,922,652; 3,055,662; 3,433,483; 3,709,498, 3,977,679; 4,015,850; 4,046,381; 4,261,574; 4,335,879; 4,346,900 and 4,436,306. However, no where in the patents cited or for that matter in the general patent literature, has it been found or is it apparent to one skilled in the art, that any of the coding techniques employed for the specific games described, can be directly applied or could have been developed to visually differentiate each and every possible numerical combination of three equally numbered dice, rolled out with equal odds, as a simplified and practical means to create a family of new dice related games that may incorporate game boards, playing cards or any combination of such paraphernalia.